diff --git a/src/main/java/eu/jonahbauer/raytracing/math/Vec3.java b/src/main/java/eu/jonahbauer/raytracing/math/Vec3.java
index 7213c96..20b8c4c 100644
--- a/src/main/java/eu/jonahbauer/raytracing/math/Vec3.java
+++ b/src/main/java/eu/jonahbauer/raytracing/math/Vec3.java
@@ -162,6 +162,10 @@ public record Vec3(double x, double y, double z) {
         );
     }
 
+    public static double tripleProduct(@NotNull Vec3 a, @NotNull Vec3 b, @NotNull Vec3 c) {
+        return a.x * b.y * c.z + a.y * b.z * c.x + a.z * b.x * c.y - c.x * b.y * a.z - c.y * b.z * a.x - c.z * b.x * a.y;
+    }
+
     public @NotNull Vec3 plus(double x, double y, double z) {
         return new Vec3(this.x + x, this.y + y, this.z + z);
     }
@@ -229,9 +233,9 @@ public record Vec3(double x, double y, double z) {
      */
     public @NotNull Vec3 cross(@NotNull Vec3 other) {
         return new Vec3(
-                this.y() * other.z() - other.y() * this.z(),
-                this.z() * other.x() - other.z() * this.x(),
-                this.x() * other.y() - other.x() * this.y()
+                Math.fma(this.y, other.z, - other.y * this.z),
+                Math.fma(this.z, other.x, - other.z * this.x),
+                Math.fma(this.x, other.y, - other.x * this.y)
         );
     }
 
diff --git a/src/main/java/eu/jonahbauer/raytracing/render/renderer/pdf/TargetingProbabilityDensityFunction.java b/src/main/java/eu/jonahbauer/raytracing/render/renderer/pdf/TargetingProbabilityDensityFunction.java
index 4b2ed62..b3611d5 100644
--- a/src/main/java/eu/jonahbauer/raytracing/render/renderer/pdf/TargetingProbabilityDensityFunction.java
+++ b/src/main/java/eu/jonahbauer/raytracing/render/renderer/pdf/TargetingProbabilityDensityFunction.java
@@ -28,7 +28,7 @@ public final class TargetingProbabilityDensityFunction implements ProbabilityDen
         var sum = 0.0;
 
         for (var target : targets) {
-            sum += weight * target.getProbabilityDensity(origin, direction);
+            sum = Math.fma(weight, target.getProbabilityDensity(origin, direction), sum);
         }
 
         return sum;
diff --git a/src/main/java/eu/jonahbauer/raytracing/scene/hittable2d/Hittable2D.java b/src/main/java/eu/jonahbauer/raytracing/scene/hittable2d/Hittable2D.java
index 9af3860..d0cb42b 100644
--- a/src/main/java/eu/jonahbauer/raytracing/scene/hittable2d/Hittable2D.java
+++ b/src/main/java/eu/jonahbauer/raytracing/scene/hittable2d/Hittable2D.java
@@ -67,13 +67,21 @@ public abstract class Hittable2D implements Hittable {
         var position = ray.at(t);
         var p = position.minus(origin);
 
-        var alpha = w.times(p.cross(v));
-        var beta = w.times(u.cross(p));
+        var alpha = Vec3.tripleProduct(w, p, v);
+        var beta = Vec3.tripleProduct(w, u, p);
         if (!isInterior(alpha, beta)) return Double.NaN;
 
         return t;
     }
 
+    protected @NotNull Vec3 get(double alpha, double beta) {
+        return new Vec3(
+                Math.fma(beta, v.x(), Math.fma(alpha, u.x(), origin.x())),
+                Math.fma(beta, v.y(), Math.fma(alpha, u.y(), origin.y())),
+                Math.fma(beta, v.z(), Math.fma(alpha, u.z(), origin.z()))
+        );
+    }
+
     protected abstract boolean isInterior(double alpha, double beta);
 
     @Override
diff --git a/src/main/java/eu/jonahbauer/raytracing/scene/hittable2d/Parallelogram.java b/src/main/java/eu/jonahbauer/raytracing/scene/hittable2d/Parallelogram.java
index da77727..e5b8086 100644
--- a/src/main/java/eu/jonahbauer/raytracing/scene/hittable2d/Parallelogram.java
+++ b/src/main/java/eu/jonahbauer/raytracing/scene/hittable2d/Parallelogram.java
@@ -1,7 +1,6 @@
 package eu.jonahbauer.raytracing.scene.hittable2d;
 
 import eu.jonahbauer.raytracing.math.AABB;
-import eu.jonahbauer.raytracing.math.Range;
 import eu.jonahbauer.raytracing.math.Ray;
 import eu.jonahbauer.raytracing.math.Vec3;
 import eu.jonahbauer.raytracing.render.material.Material;
@@ -33,10 +32,11 @@ public final class Parallelogram extends Hittable2D implements Target {
     public double getProbabilityDensity(@NotNull Vec3 origin, @NotNull Vec3 direction) {
         if (Double.isNaN(hit0(new Ray(origin, direction), FORWARD))) return 0;
 
-        var a = this.origin.minus(origin).unit();
-        var b = this.origin.plus(u).minus(origin).unit();
-        var c = this.origin.plus(v).minus(origin).unit();
-        var d = this.origin.plus(u).plus(v).minus(origin).unit();
+        var o = this.origin.minus(origin);
+        var a = o.unit();
+        var b = o.plus(u).unit();
+        var c = o.plus(v).unit();
+        var d = o.plus(u).plus(v).unit();
         var angle = PdfUtil.getSolidAngle(a, b, d) + PdfUtil.getSolidAngle(c, b, d);
         return 1 / angle;
     }
@@ -45,6 +45,6 @@ public final class Parallelogram extends Hittable2D implements Target {
     public @NotNull Vec3 getTargetingDirection(@NotNull Vec3 origin, @NotNull RandomGenerator random) {
         var alpha = random.nextDouble();
         var beta = random.nextDouble();
-        return this.origin.plus(u.times(alpha)).plus(v.times(beta)).minus(origin);
+        return get(alpha, beta).minus(origin);
     }
 }
diff --git a/src/main/java/eu/jonahbauer/raytracing/scene/util/PdfUtil.java b/src/main/java/eu/jonahbauer/raytracing/scene/util/PdfUtil.java
index 8f7b70f..739f06a 100644
--- a/src/main/java/eu/jonahbauer/raytracing/scene/util/PdfUtil.java
+++ b/src/main/java/eu/jonahbauer/raytracing/scene/util/PdfUtil.java
@@ -13,7 +13,7 @@ public final class PdfUtil {
      * must be unit vectors.
      */
     public static double getSolidAngle(@NotNull Vec3 a, @NotNull Vec3 b, @NotNull Vec3 c) {
-        var angle = 2 * Math.atan(Math.abs(a.times(b.cross(c))) / (1 + a.times(b) + b.times(c) + c.times(a)));
+        var angle = 2 * Math.atan(Math.abs(Vec3.tripleProduct(a, b, c)) / (1 + a.times(b) + b.times(c) + c.times(a)));
         return angle < 0 ? 2 * Math.PI + angle : angle;
     }
 }